9. Valuing Callable Bonds Illinois Industries has decided to borrow money by issuing perpetual bonds with a coupon rate of 8 percent, payable annually. The one-year interest rate is 8 percent. Next year, there is a 35 percent probability that interest rates will increase to 9 percent, and there is a 65 percent probability that they will fall to 6 percent. b) If the company decides instead to make the bonds callable in one year, what coupon will be demanded by the bondholders for the bonds to sell at par? Assume that the bonds will be called if interest rates rise and that the call premium is equal to the annual coupon. If interest rates rise, the price of the bonds will fall. If the price of the bonds is low, the company will not call them. The firm would be foolish to pay the call price for something worth less than the call price. In this case, the bondholders will receive the coupon payment, C, plus the present value of the remaining payments. So, if interest rates rise, the price of the

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Unformatted text preview: bonds in one year will be: P1= C + C / .09 If interest rates fall, the assumption is that the bonds will be called. In this case, the bondholders will receive the call price, plus the coupon payment, C. The call premium is not fixed, but it is the same as the coupon rate, so the price of the bonds if interest rates fall will be: P1= ($1,000 + C) + C P1= $1,000 + 2C The selling price today of the bonds is the PV of the expected payoffs to the bondholders. To find the coupon rate, we can set the desired issue price equal to present value of the expected value of end of year payoffs, and solve for C. Doing so, we find: P0= $1,000 = [.35(C + C / .09) + .65($1,000 + 2C)] / 1.08 C = $77.63 So the coupon rate necessary to sell the bonds at par value will be: Coupon rate = $77.633 / $1,000 Coupon rate = .0776 or 7.76% References and cited sources: End of Chapter Solutions Corporate Finance 8th edition Ross, Westerfield, and Jaffe Updated 12-20-2008...
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